Exploiting the quasi-linear relationship between local phase and disparity, phase-differencing registration algorithms provide a fast, powerful means for disparity estimation. Unfortunately, these phase-differencing techniques suffer a significant impediment: phase nonlinearities. In regions of phase nonlinearity, the signals under consideration possess properties that invalidate the use of phase for disparity estimation. This paper uses the amenable properties of Gaussian white noise images to analytically quantify these properties. The improved understanding gained from this analysis enables us to better understand current methodologies for detecting regions of phase instability. Most importantly, we introduce a new, more effective means for identifying these regions based on the second derivative of phase.